Mapping the Conditions for Hydrodynamic Instability on Steady-State Accretion Models of Protoplanetary Disks

Hydrodynamic instabilities in disks around young stars depend on the thermodynamic stratification of the disk and on the local rate of thermal relaxation. Here, we map the spatial extent of unstable regions for the Vertical Shear Instability (VSI), the Convective Overstability (COS), and the amplification of vortices via the Subcritical Baroclinic Instability (SBI). We use steady-state accretion disk models, including stellar irradiation, accretion heating, and radiative transfer. We determine the local radial and vertical stratification and thermal relaxation rate in the disk, which depends on the stellar mass, disk mass, and mass accretion rate. We find that passive regions of disks-that is, the midplane temperature dominated by irradiation-are COS unstable about one pressure scale height above the midplane and VSI unstable at radii > 10 au. Vortex amplification via SBI should operate in most parts of active and passive disks. For active parts of disks (midplane temperature determined by accretion power), COS can become active down to the midplane. The same is true for the VSI because of the vertically adiabatic stratification of an internally heated disk. If hydrodynamic instabilities or other nonideal MHD processes are able to create a-stresses (> 10(-5)) and released accretion energy leads to internal heating of the disk, hydrodynamic instabilities are likely to operate in significant parts of the planet-forming zones in disks around young stars, driving gas accretion and flow structure formation. Thus, hydrodynamic instabilities are viable candidates to explain the rings and vortices observed with the Atacama Large Millimeter/ submillimeter Array and Very Large Telescope.